we refer to [1]}, [2]}, [3]}, [4]} for the modelling. In the Richards
equation (REF ), the function \(k : [0,1] \rightarrow \mathbb {R}\)  is
the permeability function which has to be determined from
experiments, \(g\)  is the gravitational acceleration, \(e_z\)  is the
normal vector pointing upwards. It is always assumed that \(s\)  takes
only values in \([0,1]\) .
